Fault-tolerant cycle embedding in dual-cube with node faulty

A low-degree dual-cube was proposed as an alternative to the hypercubes. A dual-cube DC(m) has m+1 links per node where m is the degree of a cluster (m-cube) and one more link is used for connecting to a node in another cluster. There are 2^m+1 clusters and hence the total number of nodes is 2^2m+1 in a DC(m). By using Gray code, we show that a DC(m) is (m-1)-link Hamiltonian and there exists a faulty-free cycle containing at least 2^2m+1-2f nodes with f≤m-1 faulty nodes.